Karen Uhlenbeck Becomes First Woman To Win Abel Prize in Mathematics

Karen Uhlenbeck (formerly of University of Texas at Austin and now at Princeton's Institute for Advanced Study) has become the first woman to win the Abel Prize. The Abel Prize has been awarded since 2003 by the Norwegian Academy of Science and Letters and comes with a check for 6 million Norwegian kroner (about US$700,000).

Uhlenbeck, 76, is cited for her "pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics."

The American Mathematics Society states:

Uhlenbeck is a former MacArthur Fellow, a Fellow of the American Academy of Arts and Sciences, a recipient of the National Medal of Science (2000) and the Steele Prize for Seminal Contribution to Research (2007), and a member of the inaugural class of AMS Fellows. She is the first woman mathematician to be elected to the National Academy of Sciences (1986) and the second woman to give a plenary lecture at the International Congress of Mathematicians (1990—Emmy Noether was the first). In "The Abel Prize Laureate 2019," Uhlenbeck observes that she is a role model but "it’s hard, because what you really need to do is show students how imperfect people can be and still succeed. ... I may be a wonderful mathematician and famous because of it, but I’m also very human.” Uhlenbeck was the Sid W. Richardson Foundation Regents' Chair in Mathematics before retiring from the University of Texas at Austin in 2014, and is now a visiting senior research scholar at Princeton University and a visiting associate at the Institute for Advance Study. See more about her work in the March Notices article, "Karen Uhlenbeck and the Calculus of Variations," by Simon Donaldson,  and on the Abel Prize website, which has the full prize citation, her biography, descriptions of her work, and a video of the announcement of the prize.

Congratulations to Professor Uhlenbeck!

NEWS: United States Places First In International Mathematics Olympiad

The U.S. team won first place at the 59th International Mathematical Olympiad (IMO), which took place in Cluj-Napoca, Romania on July 3-14, with 116 countries and 615 students participating. The USA Mathematical Olympiad Team cosisted of: Adam Ardeishar, Andrew Gu, Vincent Huang, James Lin, Michael Ren, and Mihir Singhal.  Individually they also took home five gold medals (Lin scored a perfect 42) and one silver medal. Gu, Huang, and Lin are returning IMO team members from 2017. Teams from Russia and China placed second and third, respectively

Hat/tip to American Mathematics Society and Mathematical Association of America.

Happy 241st Birthday, Carl Friedrich Gauss!

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Carl Friedrich Gauss is one of the most important mathematicians of all time. Today, April 30th, is the 241st anniversary of his birth, and Google's Doodle is recognizing that fact. Some of the reasons why Gauss is known as the "Prince of Mathematicians" (in Latin princeps mathematicorum);

• Proved the fundamental theorem of algebra (in his Phd thesis!)
• Proved that a 17-sided polygon (the heptadecagon) coudl be created with compass and straigh-edge.
• Invented the Diiscrete Fourier Transform (160 years before Cooley and Tukey)
• Proved Fermat's Last Theorem (for n=3 and n=5)
• Computed the sum of the 100 positive integers (at age 5!)
• The normal distribution is also known as the Gaussian distribution

And many, many more...

Harvard University Mathematics Department Hires SECOND EVER Female Tenured Full Professor

Harvard University is considered the acme of most things academic, with its 37 billion dollar endowment and its perennial placement at the top of the college rankings. The  Mathematics department at Harvard is not the very best in the country (that distinction usually goes to Princeton University) but it is definitely well-known. The fact that they have been atrocious in the area of doversity for so long is widely known.

This week comes news that things are starting to change at Harvard, as they announced they have hired their second ever tenure female full professor, ending a six-year stint in which they literally had zero tenured female professors (by contrast Princeton has had two senior female math professors for years: Maria Chudnovsky and Sun-Yung Alice Chang).

The Daily Crimson reports:

University of California at Berkeley math professors Lauren K. Williams ’00 and Denis Auroux will join Harvard’s math department as senior faculty at the start of the next academic year, Department Chair Curtis T. McMullen said in an interview last week. 

Auroux has served as a math professor at UC Berkeley since 2009 and has published articles on subjects ranging from “symplectic submanifolds” to “Lefschetz pencils.” Williams, a former math concentrator, won a tenured associate professorship at UC Berkeley in 2013—and a full tenured professor position there in 2016—and has written extensively about cluster algebras and tropical geometry.

As a friend of mine said on Twitter this weekend in commenting on the news. "It's 2018."

CELEBRITY FRIDAY: LGBT Mathematician Moon Duchin Wins Prestigious Guggenheim Fellowship

Moon Duchin is an out lesbian mathematics professor at Tufts University who has just become the sole pure mathematician in the 2018 class of Guggenheim Fellows. Here's the official announcement:

Moon Duchin is a mathematician at Tufts University, where she is also a Senior Fellow in the Tisch College of Civic Life and serves as the founding director of the interdisciplinary program in Science, Technology, and Society. She majored in Mathematics and Women's Studies at Harvard and received her PhD in Mathematics from the University of Chicago. 

Duchin's research in pure math lies in geometric group theory, low-dimensional topology, and dynamics. An area of particular interest is nilpotent geometry, or the shape of groups that fail to be commutative in a controlled way. She has studied random walks, random groups, and rigidity theorems for surfaces and billiards. She is also interested in the social studies of science, particularly the role of expertise, authority, intuition, and proof. 

Duchin is currently engaged in a long-term project on the geometry of gerrymandering, an application of mathematics to civil rights. She has worked to build a national network of collaborators doing wide-ranging work on mathematical and computational interventions in electoral redistricting. They aim to engage the legal, political, and philosophical dimensions of the gerrymandering problem, working closely with civil rights organizations. Duchin recently served as a consultant for the governor of Pennsylvania in the court-mandated push to redraw the congressional map.

I know Moon relatively well, having spent a 3 days attending the latest Geometry of Redistricting Workshop at the University of San Francisco last month. I'm not surprised she has been recognized by the Guggenheim Foundation, I think that she should also be considered for an even more prestigious award, the MacArthur Foundation Fellowship, in the near future.

Congrats, Moon!

REPORT: Boys and Girls Equally Interested In STEM; Boys More Prepared

In a new report from ACT (yes, the organization that runs those other college readiness tests) there is a result that states that all though boys and girls have an equal interest in careers in science, technology, engineering and mathematics (STEM), it turns out that boys are generally more prepared for them.

Ed Week reports:

To determine readiness, students were assigned a STEM score based on combined results from their ACT math and science tests. ACT test scores range from 1 to 36. A student earning at least the benchmark score of 26 has a 50 percent chance of earning a B or higher in first-year college STEM courses, and a 75 percent chance of earning a C or higher, according to the report. The student is also more likely to stick it out with a STEM major and earn a bachelor's degree.  

The report revealed that just 18 percent of females, compared to 24 percent of males, earned a score of 26. 

The disparity is even larger among students with an interest in STEM: 22 percent of females earned a score of 26 compared to 31 percent of males. Even more surprising, females interested in STEM were less likely than all males (including those with or without an interest in STEM) to meet or surpass that benchmark score (22 percent versus 24 percent). Meanwhile, the overall level of interest in STEM between females and males is nearly equal at 47 percent versus 50 percent, respectively.

The source of the data is from the 2 million students who took the ACT in 2017.

STUDY: U.S. Mathematics Majors Most Likely To Switch To Another Subject

The National Center for Education Statistics at the U.S. Department of Education released a report at the end of last year about students switching majors in college. "Beginning College Students Who Change Their Majors Within 3 Years of Enrollment" has a number of interesting facts about students who change majors while pursuing associate's and bachelor's degrees in the United States:

• About half (52 percent) of students whose original declared major was mathematics switched majors within 3 years. Mathematics majors changed majors at a rate higher than that of students in all other fields, both STEM and non-STEM, except the natural sciences.
  
• Within 3 years of initial enrollment, about 30 percent of undergraduates in associate’s and bachelor’s degree programs who had declared a major had changed their major at least once.
  
• About one-third of students enrolled in bachelor’s degree programs changed majors, compared with 28 percent of those enrolled in associate’s degree programs.
  
• About 1 in 10 students changed majors more than once: 10 percent of associate’s degree students and 9 percent of bachelor’s degree students.

Hat/tip to Voice of America!

Today is 2/7/18, or "e Day!"

Today is February 7, 2018, or 2/7/18 in common date notation, so it  is also known as "e Day." The first 4 digits of the mathematical constant,e, are 2.718, so just like Pi Day is celebrated on March 14 (3/14) today is the day we recognize another very important number, which is the base of the natural logarithms and is often called "Euler's number." It appears in one of the most beautiful equations in all of mathematics:

This amazing equation has the Euler's number, the base of the complex numbers, i, the number π and the numbers 1, 0 as well as the symbols = and +!

Happy e day!

Lost Einsteins: New Report Demonstrates Variation In Innovation Opportunity by Class, Race and Gender

There’s an interesting new report (from Stanford’s Raj Chetty) showing how lack of diversity in STEM is leading to reduction in the number of innovations being created in this country, even by low-income children who would be expected to be inventors due to their proficiency in math in school. (Generally proficiency in mathematics is a predictor of patent filing.) The report calls the result of this gap “Lost Einsteins.”

The New York Times wrote about this latest report this week:

The researchers worked with the Treasury Department to link the tax records with patent records. Doing so allowed them to study the backgrounds of patent holders (and the study focused on the most highly cited, significant patents). The researchers — Chetty, Alex Bell, Xavier Jaravel, Neviana Petkova and John Van Reenen — were also able to link these records to elementary-school test scores for some patent holders.

Not surprisingly, children who excelled in math were far more likely to become inventors. But being a math standout wasn’t enough. Only the top students who also came from high-income families had a decent chance to become an inventor.

This fact may be the starkest: Low-income students who are among the very best math students — those who score in the top 5 percent of all third graders — are no more likely to become inventors than below-average math students from affluent families.

Here is a graphic which demonstrates the difference in patent-holding by income level.

Of course there is also variation by race and by gender as well:

This report explains why broadening the participation in STEM is so important. As Chetty says "There are great differences in innovation rates. Those differences don’t seem to be due to innate ability to innovate.”

Our goal should be to make sure that the difference in innovation rates are not related to race, gender or income.

OCTOBER 23-27 IS #ACTIVELEARNINGWEEK2017

This week is Active Learning Week. If you're a college professor, you can take a pledge.

CELEBRITY FRIDAY: Katherine Johnson (from Hidden Figures) Turns 99!

Katherine Johnson, the NASA “computer” whose life story was the primary motivation behind the hit book Hidden Figures by Margot Lee Shetterly turned 99 years old yesterday! She was played by Taraji P. Henson in the movie adaptation (see my review) that was nominated for multiple academy awards earlier this year. Last year NASA renamed a building after her on the occasion of her 98th birthday and before that, President Obama awarded her the National Medal of Freedom.

Hat tip to Vanity Fair

CELEBRITY FRIDAY: Maryam Mirzakhani, Only Female Fields Medalist, Has Died

Maryam Mirzakhani, Stanford mathematics full professor and Fields medalist, died last Friday July14 of breast cancer at the age of 40.  The Fields medal is the highest international honor in Mathematics (the equivalent of a Nobel prize) and Mirzakhani was the first (and only woman) to have received the award.

The loss of Mirzakhani (at such an early age) has stunned the mathematics community and resulted in a deluge of press. Here's an excerpt from the New York Times obituary:

Maryam Mirzakhani, an Iranian mathematician who was the only woman ever to win a Fields Medal, the most prestigious honor in mathematics, died on Friday. She was 40.

The cause was breast cancer, said Stanford University, where she was a professor. The university did not say where she died.

Her death is “a big loss and shock to the mathematical community worldwide,” said Peter C. Sarnak, a mathematician at Princeton University and the Institute for Advanced Study.

The Fields Medal, established in 1936, is often described as the Nobel Prize of mathematics. But unlike the Nobels, the Fields are bestowed only on people aged 40 or younger, not just to honor their accomplishments but also to predict future mathematical triumphs. The Fields are awarded every four years, with up to four mathematicians chosen at a time.

She will be  missed!

CELEBRITY FRIDAY: Katherine Johnson, Legendary NASA Mathematician, Turns 98 Today

Katherine Johnson is an African-American mathematician who is famous for contributing calculations to several landmark NASA missions. Johnson turns 98 today, and was awarded the National Medal of Freedom by President Barack Obama in November 2015. In May 2016, NASA named one of its buildings at the NASA Langley Research Center the Katherine G. Johnson Computational Research Facility.

Johnson worked at Langley from 1953 until her retirement in 1986, beginning as a research mathematician -- part of a pool of women hired to perform mathematical equations and calculations by hand for engineers. She quickly distinguished herself and was permanently assigned to the branch that would later calculate the launch windows for NASA’s first Project Mercury flights. 

Notable accomplishments include her computation, by hand, of the launch window and trajectory for Alan Shepard’s maiden space voyage aboard Freedom 7 in 1961, and verification, also by hand, of calculations made by the first computers for John Glenn's history-making orbit around the Earth in 1962. She also calculated the trajectory for the historic Apollo 11 first moon landing flight in 1969.

In January 2017, a big-budget Hollywood movie titled Hidden Figures starring Oscar-winner Octavia Spencer, Taraji P. Henson, Janelle Monae, Kevin Costner, Kirsten Dunst and Jim Parsons based on the real-life story of Johnson and other Black women who worked for NASA will be released in theaters. See the trailer below:


Happy Birthday Katherine Johnson!

Mathematical Analysis Reveals TYRION Is Main Character of Game Of Thrones

This is really cool! io9 reports on a mathematical analysis of the third book in the A Song of Ice and Fire series by George R.R. Martin to demonstrate that the Tyrion Lannister is the actual main character of the series.

After ranking the characters through various methods, the three most common characters that could be perceived as the “main” stars of the series emerged: Sansa Stark, Jon Snow, and—at the top in pretty much every measured regard—Tyrion Lannister. 

It’s not really that surprising—each chapter of a book in the series is told from the perspective of a different character, and Tyrion has the most chapters to his name across the whole saga. 

The type of mathematics being deployed here is called "network science." You can read the text of the original article (titled "Network of Thrones") at Math Horizons.

EYE CANDY: Pietro Boselli (4th Time!)

Pietro Boselli has appeared as Eye Candy on this blog three times before (April 27, 2015, July 6, 2015, and December 7, 2015), thus with today's appearance he will become one of the rare 4-time Eye Candy models. Although my preference would be to always display pictures of phyne bruthas or hot papis, I have to admit that there are a lot of cute white boys out there. Part of the reason why Boselli has appeared so often on this blog is that he has a unique (easily googled) name and he has appeared in a lot of stunning photographs that are all over the web. And there's the fact that we have something in common: we both know (and teach) advanced mathematics!

The pictures featured above are from a new set taken for British gay magazine Attitude shot by Daniel Jaems.

Enjoy!

Pres. Obama Invites L.A. Teen With Perfect AP Calc Score To White House Science Fair

Cedrick Argueta, 17, is in the news this week because the Lincoln High School senior was one of barely a dozen students to earn a perfect score on his Advanced Placement Calculus AB exam. This is quite an achievement, since over 300,000 students take the exam every year. Even President Obama noticed and invited Cedrick to the White House Science Fair.

The Los Angeles Times reports about the reaction to Cedrick's achievement:

Cedrick — a quiet, humble student who is quick to thank his teachers and parents for his success — said he'll join the president at the fair “if his offer still holds.”
The White House Science Fair, hosted by the president, features projects, designs and experiments from students across the country and celebrates students who excel in science, technology, engineering and math.
Cedrick's story has made headlines around the world since his score was announced by the Los Angeles Unified School District last week. He is the son of Lilian and Marcos Argueta, both of whom came to the United States as young adults — she from the Philippines, he from El Salvador. Lilian, a licensed vocational nurse, works two jobs at nursing homes, and Marcos is a maintenance worker at one of those nursing homes.
“I'm speechless,” Lilian Argueta said Sunday. “I can't believe this is happening.”
Lincoln High School Principal Jose Torres said Cedrick's achievement was inspiring.

I love this story! Lincoln High School is roughly 2 miles from my house and as a professor of Mathematics I interact with students who have taken AP Calculus exams before coming to my college. And I have taught the material on this exam to my students many times. That Cedrick got every single point on the exam is quite amazing, and inspiring!

Merry X-Mas!

This is a fun (mathematical) way to wish everyone Merry X-Mas!

EYE CANDY: Pietro Boselli (3rd time!)

Pietro Boselli has appeared as Eye Candy twice before (April 26, 2015 and July 6, 2015). Boselli, you may recall, is the Italian mathematics Ph.D. student who made headlines around the world when one of his students realized their maths instructor was also a smoking hot male model and posted the news to social media and it went viral. 

I think part of the reason why the story got so big is that Boselli is so hawt, don't you?

WATCH: Animated Gif Proving Pythagoras' Theorem #math

This is a perfect depiction of a creative way to illustrate mathematical concepts, even relatively simple ones like Pythagoras' Theorem that a² + b² = c². Or, in words, the sum of the squares of the two sides of a right-triangle is equal to the square of the hypotenuse.

Mathematical Analysis of Women's Tennis Open-Era Challenges Serena's GOAT Status

On the eve of the start of her campaign to secure her 22nd major title, fourth of the year, Serena Williams's claim to the title of Greatest of all Time is being analyzed in an article at Five Thirty Eight titled "Serena Williams And The Difference Between All-Time Great And Greatest Of All Time." The article uses a particular mathematical technique called computing an ELO rating to assign a number (which varies over time) to the relative strength of players in head-to-head competition. The graph of all the major champions (Navratilova, Evert, Graf, Seles, Henin, Venus and Serena) are depicted.

From the graph it can be shown that Serena does not achieve the highest ELO rating of all time.

Elo definitely puts Williams in the top tier of female tennis players, but it tells a slightly more muted story than other measures. In particular: While Williams has been great, and has been doing unprecedented things for a player of her age, the relative weakness of the tier of players beneath her undermines her GOAT claim. 

The possibility that Serena has benefited from “weaker competition” is pretty conventional, and certainly debatable, but Elo gives us a useful way to examine exactly what that possibility means and what it implies.
For the unfamiliar, Elo is a rating method originally developed for chess, but eminently suitable for tennis. It’s very simple: Two players enter a match with Elo ratings based on their prior results. Elo uses their ratings to predict their head-to-head outcome, and then updates those ratings depending on the outcome.² It’s not without limitations: Elo makes every head-to-head prediction based solely on the two players’ ratings, which, in turn, are only affected by previous match results.

However, one aspect of Serena which makes her career unique is her 2nd peak in her ELO rating, which has happened at an unprecedented stage of her career, in her 30s. It also claims that Serena was at her best in 2003 (when she won her first Serena slam).

I understand that these results will disappoint some and encourage others but I appreciate the analysis in that bring at least a measure of quantitative rigor to a discussion which is essentially Qualitiative and subject in nature: Who is the Greatest of all Time? In my mind, the figures STILL indicate hat the answer is Serena Williams.